Posted
by
kdawson
on Tuesday August 05, 2008 @09:43PM
from the shannon's-cat dept.

KentuckyFC writes "One of the cornerstones of modern physics is Claude Shannon's theory of communication, which he published in 1948. If you've ever made a phone call, watched TV, or used a computer, you've got Shannon to thank for describing how information can be moved from one place in the universe to another using an idea called the channel capacity. But nobody has been able to develop a quantum version of this theory. So physicists have no idea how much quantum information can be sent from one point to another. Now two American physicists have made an important breakthrough by proving that two quantum channels with zero capacity can carry information when used together. That's interesting because it indicates that physicists may have been barking up the wrong tree with this problem: it implies that the quantum capacity of a channel does not uniquely specify its ability for transmitting quantum information (abstract). And that could be the idea that breaks the logjam in this area."

Does this mean we can now send messages instantaneously using quantum entanglement? You have two particles that are entangled, each producing the same sequence of random values when measured. If we have two pairs of entangled particles, we have two channels and can therefore communicate faster than light speed?

There are plenty of reasons why people don't understand quantum mechanics. Most people just don't care.

But I can list plenty of better reasons, for example, Calbi-Yau space. If you imagine the rubber-sheet model of the universe that everyone has seen in physics, replace it with this instead. Its pretty accurate as far as the math goes, and is a spin-off of QM. And then there are all of the various thought experiments, like Schrödinger'

Yes, both channels have a non-zero capacity of transferring classical information. One of them even has a non-zero capacity for transferring secret information. What is not possible is to trasfer even a single qubit of quantum information without significant error, given as many uses of the channel you like and any quantum error correction procedure you can imagine.

My (preliminary) understanding of the example is that one of the channels (the symmetric one) allows the secret information of the other to be

So, does that mean they could somehow be used with entangled photons or whatever to transmit information faster than light?

No, since you need to encode something in the channels, and you can't entangle a photon, send it off to the receiver and then change your photon's quantum state at a later date to encode anything in a way which gets information to the other party; the best you can do is measure them and go "woa, they're highly correlated!".

The paper talks about two types of capacity a quantum channel can provide; "private capacity", which is our common or garden secure crypto channel, and "assisted capacity", whereby you ex

>> "two quantum channels with zero capacity can carry information"> Feynman once said that nobody understands quantum mechanics, and this is why.

No. Nobody "understands" quantum mechanics because it is illogical. It is chock full of applications of the mind projection fallacy [overcomingbias.com], starting with its premises and going all the way to the conclusions (some of which just happen to be correct for other reasons).

In a way you can have the same thing with two conventional channels. If your SNR is just bad enough that you can't recover any useful information from one channel, under some measurements you would say that channel has zero capacity. If you transmit the same signal on a second channel, then average the two, you improve your SNR by sqrt(2), making it recoverable, so the combined channels have a non-zero capacity.

At the end of my Physics degree, I had the option of continuing in Physics academia, or going into the world of work.
I'm sad to say that the main reason I wanted to leave Physics, despite somehow managing to retain a small fragment of my initial enthusiasm for the subject, was looking round at the professional physicists who took my course, and realising I really didn't want to spend the rest of my productive life surrounded by these people.

Great demonstration. I couldn't have -not- said it better myself. It is something that is true in other areas and the relation ship of two zeros does have an effect on the outcome == 8 or perhaps infinity.

I'm not sure how useful this is. The summaries seem to say that if you take two or more channels that have a signal to noise ratio of zero, there's some potential for binding them into a useful channel, but there's no indication of what kind of recovery rate there can be gained from this. Is this just error-correction applied to an extreme?

If you want to be useless to people, you can't simply feed them *wrong* information, because once they realize you always give them wrong information, you become *more* useful to them, because they can simply invert everything you say (i.e. assume it's false), to extract useful information.

So, to be useless, you have to keep giving, not *wrong* information, but *random* information -- sometimes true, sometimes false, so they can't extract any "si

Not a S/N ratio of zero, their definition of channel capacity is only very tenuously connected to Shannon's channel capacity really. Quantum channels already have 0 capacity at non zero fidelity (the quantum equivalent to S/N). The 0 capacity channel from this paper aren't 0 capacity because of their fidelity though, the channels are 0 capacity for different reasons.

The recent Amateur radio mode called WSPR [princeton.edu] ('whisper') can work with a signal around 27 dB below the noise (SNR of -27dB). This site [wsprnet.org] records contacts between hams worldwide in real time. Most activity is on 30m.

Most submissions to ArXiv do get submitted to peer-reviewed journals; this one claims to have been submitted in June (although they don't specify where). It's an opportunity for researchers to share their work without the delay of waiting for publication. Usually, papers there do get revised after going through the referee process.

We also get news from blogs, apple fan sites, and wikileaks. Non of those is peer reviewed either. The point is that it's not that people should take articles sourcing ArXiv with a grain of salt; it's that they should take everything with a grain of salt.

You can xor a random pad of 1s and 0s with some copyrighted data, and end up with a block of data which looks totally random. Neither the random pad or the encrypted block have any useful information when taken apart, but together they contain all the information of the copyrighted work.

Copyright is metadata. All you're saying is that encrypting a copyrighted work with a one-time-pad doesn't remove the copyright. Which is trivially true, since the copyright is not contained in the data.

Think of copyright like the chain of custody that you have to maintain in a court case. If you use a non-licensed agent to gather data, it weakens your case, even though the data is the same whether the agent is licensed or not... as the RIAA has recently discovered.:)

I think that Khashishi has got the essence of the 0+0>0 thing here. I haven't completely penetrated the noise in the Smith/Yard ArXiv article yet, but I'd bet my money that it boils down to this:

Take two channels in each of which all bits are completely random, and independent of the information that you wish to send. Let each bit of your information determine the correllation or anticorrellation of corresponding bits in the two channels, by introducing a quantum constraint between them before their actual random values are determined. Then, as in Khashishi's description, the xor of the two random channels is the message.

The only difference I detect in Smith/Yard vs. Khashishi is that they use quantum trickery to make the whole thing look symmetric. Neither of the random channels predates the other. Each one, evaluated singly, appears to be completely independent of the encoded message. In Khashishi's description, the time sequence in the construction of the two random sequences makes one of them seem a priori random, and the other to be a one-time pad encoding of the message, while in the Smith/Yard article you can't tell which is which.

It seems more like a meretricious way of telling a causal story about a well-known phenomenon than something truly "essentially quantum."

In Khashishi's description, the time sequence in the construction of the two random sequences makes one of them seem a priori random, and the other to be a one-time pad encoding of the message, while in the Smith/Yard article you can't tell which is which.

One-time pad ciphertext does appear to be random. Shannon proved that it has perfect secrecy.

<quote>One-time pad ciphertext does appear to be random. Shannon proved that it has perfect secrecy.

</quote>

Right. But Smith/Yard make a stronger claim than randomness. They claim that the content of each channel does not depend on the message at all. Once the one-time pad is determined, the encoded message is determined completely by the plaintext. By encoding the plaintext into a quantum entanglement prior to the creation of either random channel, they are able to tell a story in which each c

The data looking random or not has nothing to do with the information capacity of the channel.
Shannons definition of information capacity is simply the maximum amount of information that can be recovered by the receiver on the channel.
A channel where the receiver can't recover data under any circumstances is a 0 capacity channel, that reason could be interfering noise or the fact that the channel doesn't exist.
Which poses a problem with this theory, it basically says 2 channels that don't exist can trans

So basically all you have to do is qualify any theory with the word "quantum" and you can justify anything. Two channels that don't exist can all of the sudden transmit information. All of the sudden 0 + 0 = something more than 0. If this quantum stuff ever takes off then we are all in trouble. We'll have human sacrifice, dogs and cats living together... mass hysteria!

The data looking random or not has nothing to do with the information capacity of the channel.Shannons definition of information capacity is simply the maximum amount of information that can be recovered by the receiver on the channel.A channel where the receiver can't recover data under any circumstances is a 0 capacity channel, that reason could be interfering noise or the fact that the channel doesn't exist.Which poses a problem with this theory, it basically says 2 channels that don't exist can transmit

Harry "Hello Jim Im ringing you back regarding the message you left on my voice mail."
Jim "What message ? I hevent left one yet"
Harry "Aw crap I did it again, I will never get my head around our new quantum telephone system"

Interesting, but the paper seems to have a nasty habit of simply redefining what "capacity" means in a quantum context, to basically, "Well, if we have two interacting channels, one changes the other to have non-zero capacity." And if I interpret it that way, it simply rewords the problem to be different from the original interpretation. Also, there's a significant amount (even for an arxiv paper) of speculation present (which is interesting!). From the paper: Nonetheless, each channel hasthe potential to \activate" the other, effectively cancel-ing the other's reason for having no capacity. We knowof no analog of this effect in the classical theory. Per-haps each channel transfers some different, but comple-mentary kind of quantum information. If so, can thesekinds of information be quantfied in an operationallymeaningful way? Are there other pairs of zero-capacitychannels displaying this effect? Are there triples? Doesthe private capacity also display superactivation? Whatnew insights does this yield for computing the quantumcapacity in general?

One "classical" analogy is that of orthogonally-crossed polarizers, which, upon insertion of another polarizer with principle axis somewhere between that of the originals, will allow light to shine through where none was before.

Because quantum information can be negative it would seem this theory could be applied to make a channel with 0 negative capacity have some cpacity from nothing in the same way.
So really any extra positive capacity could be cancelled out.